Unsteady simple shear flow in a viscoplastic fluid: comparison between analytical and numerical solutions

Abstract In this paper, an unsteady flow of a viscoplastic fluid for simple shear flow geometry is solved numerically using two regularizing functions to overcome the discontinuity for zero shear rate of the Bingham constitutive law. The adopted models are the wellknown Papanastasiou relation and one based on the error function. The numerical results are compared with the analytical solution of the same problem obtained by Sekimoto (J Non-Newton Fluid Mech 39:107– 113, 1991). The analysis of the results emphasizes that the errors are much smaller in the yielded than in the unyielded region. Themodels approximate closer the ideal Bingham model as the regularization parameters increase. The differences between the models tend to vanish as the regularization parameters are at least greater than 105.